Gaming Guru

Are You Overestimating Your Chances of a Hit?

How often, at video poker, have you started with what you thought a strong
four cards to a straight, flush, or straight flush, then got zonked?
Probably enough to wonder whether something you said to a slot attendant
had the casino tightening the payout screws.

There are no such screws, of course. The problem, common to most forms
of gambling, is that few solid citizens have much of a grasp on the
likelihoods of the outcomes they either desire or dread. Completing a
four-card straight, flush, or straight flush ought to be a piece of
cake. Right? Well, let's see.

Take a double-ended outside straight such as 4-5-6-7, mixed suits,
nothing wild. You've seen five cards -- four you've held, one you
tossed. So 47 remain in the 52-card virtual deck. To win, you need any
of eight cards, four threes or four eights. Your outlook is to average
eight hits in 47 tries, only 17 percent.

Inside and single-ended outside straights, for instance 4-6-7-8 and
A-2-3-4, respectively, are even tougher to complete. With nothing wild,
only one rank -- four possibilities -- will do the trick: any five in
either of these cases. The prognosis for success is four out of 47, a
mere 8.5 percent.

If you play jacks or better and hold one or
more face cards, you can miss the straight and salvage your bet on a
high pair. With 8-9-10-J, the chance is three in 47 -- almost 6.5
percent -- of pairing the jack. With 9-10-J-Q, six cards yield a high
pair, twice as good at nearly 13 percent. And 10-J-Q-K offers nine ways
out of 47, over 19 percent; this is 17 plus 19 or 36 percent in all.
J-Q-K-A is superior from the high pair perspective, but is single-ended
and costs you 8.5 percent on the possible straight.

Perhaps you prefer joker-poker. Now, 4-5-6-7 means you need the joker or
any three or eight -- nine out of the 48 remaining, or close to 19
percent. Easier, but not by much. If one of the cards you hold is the
joker, your prospects depend on where it is. On an end is best. For
example 5-6-7-X completes with any three, four, eight, or nine. This is
16 out of 48 or 33 percent. In the middle, maybe 5-X-7-8, you'd win with
any four, six, or nine: 12 out of 48 or 25 percent. A joker in the hand
also beats one in the deck because matching any hard rank already held
yields triplets; that's nine cards out of 48, around 19 percent chance.

How about flushes? When nothing's wild, starting with four of the same
suit means nine are left in the 47 remaining cards. Your chance is nine
out of 47, just over 19 percent. With one joker wild, this goes up to 10
out of 48 -- roughly 21 percent. One of the four cards you hold already
being the joker doesn't change the probability of a flush. You've used
three of the target suit so 10 are left in the 48 remaining cards. But,
as with a joker and three to a straight, you can make triplets if the
flush falls through, with the chance also being nine out of 48 or 19
percent.

Possible straight flushes offer more possibilities. Say your game is
nothing wild. Your top shot would be an outside four-card possible
straight flush. Considering high pairs, best is a suited 10-J-Q-K. You
have two ways out of 47, 4.25 percent, to make the straight flush. This
leaves seven ways out of 47 (almost 15 percent) for a flush, six out of
47 (nearly 13 percent) for a straight, and the same 19 percent for a
high pair. That's close to 51 percent in all. An inside or single-ended
straight flush drops you to one card out of 47 for the straight flush
and three out of 47 for the straight, 2.1 and 6.4 percent, respectively.
The chance of a flush is again nine out of 47, or 19 percent.

With a joker, the hardiest four-card possible straight flush is the
5-6-7-X type. Four cards make a biggie (8.3 percent), 10 a flush (20.8
percent), 12 a straight (25 percent), and nine trips (18.8 percent) --
72.9 percent prospects of at least some return.

So it's in probabilities, which aren't all that high, not in how you
talk to slot attendants. But, be gracious to those who serve you in the
casino anyway. As the poet, Sumner A Ingmark, advised:

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